Spin reorientation maneuver for spinning spacecraft

ABSTRACT

A method for controlling reorientation of a spacecraft&#39;s spin from a minor axis spin bias to a desired major axis spin after spin transition. A control system monitors rotational rates about the principal axes to detect a separatrix crossing of a polhode path therein. Controlled thruster firings resulting from spin rate information successively decrease and increase a characteristic parameter and capture the spacecraft during a spin transition to a desired major axis bias orientation. It is possible to monitor only ω 1  and ω 3  in an alternate embodiment.

BACKGROUND OF THE INVENTION

The present invention relates generally to methods for controlling spinreorientation of spinning spacecraft. More specifically, the presentinvention relates to affecting a spin transition of a spacecraft from aminor axis spin to a particular major axis spin orientation.

A single-body spacecraft having energy dissipation and which spins abouta minor axis is directionally unstable. Active control, such as rocketmotors or dampers on despun platforms, stabilize such a spacecraft.Removal of these stabilizing mechanisms permit the spacecraft toreorient its principal spin axis and begin to rotate about its majoraxis. The reorientation results from energy dissipation, including fuelslosh and vibration. Spin transition is the term coined for thisreorientation maneuver from a spin bias about a minor spin axis to aspin bias about a major spin axis.

FIG. 1 is a graphical representation of a spacecraft 10 with a majoraxis X, an intermediate axis Y, and a minor axis Z. The major axis Xcoincides with a principal moment of inertia axis having the largestinertia, I₁. The minor axis Z is orthogonal to the major axis X andcoincides with a principal moment of inertia axis having the smallestinertia, I₃. The intermediate axis Y is orthogonal to both the majoraxis X and the minor axis Z and coincides with a principal moment ofinertia having an intermediate inertia, I₂. For virtually all real worldspacecraft, I₁ >I₂ >I₃.

Spin rates, either positive or negative, about the X axis, Y axis, orthe Z axis are, respectively, ω₁, ω₂, and ω₃. Spacecraft often arepurposefully and initially rotated about the minor axis Z for severalreasons. First, launch vehicles have fairings which constrain or requirethat a long and narrow axis of the spacecraft, that is, the Z axis, bealigned with the longitudinal axis of the launch vehicle. The launchvehicle typically spins longitudinally prior to separation and resultsin a minor axis spin rate for the spacecraft 10 after separation.Second, when a rocket motor is used for orbit raising, the rocket motorand spacecraft combination is spun about the minor axis to increasestability during the firing and orbit raising. When the firing iscompleted, the combination undergoes spin transition.

Spin transition has some problems. One problem is that orientation ofthe spacecraft relative to an inertially-fixed angular momentum vectorat the completion of the spin transition maneuver cannot be determinedin advance with any degree of accuracy. In other words, the spacecraft10 has either a positive or a negative spin about the major axis X.Physically, this corresponds to two final attitudes which are 180°apart. Either face A or face B (of FIG. 1) will present itself in thedesired direction. Many spacecraft 10 have sensitive on-boardinstruments which must be shielded from the sun or have directionalcommunication equipment which must point towards the earth. In both ofthese situations, ensuring a final spin polarity about the major axis isnecessary.

Prior art techniques of optimal reorientation for a spacecraft 10 forattitude acquisition using momentum wheels have been developed. In termsof fuel usage, the passive sign transition maneuver is optimal, andmomentum wheels, with their attendant complexity, are not required. Tomake the maneuver truly useful, however, the final spin polarity must becontrolled, requiring some fuel expenditure. Conventional methodsattempt to control the spacecraft during spin transition to preventoccurrence of an improper orientation.

SUMMARY OF THE INVENTION

The present invention provides a method for effecting spin transition ofa rotating object from a spin about a minor axis to a particular spinabout a major axis by permitting passive spin transition and afterwarddetermining if the final orientation will be correct while assertingactive control only upon an indication of an incorrect orientation.

In a specific embodiment, a detected sign change in ω₃ establishes anoccurrence of a spin transition. Testing ω₁ determines if the spacecrafthas the desired sign for the major axis. Subsequently, if ω₁ has thewrong sign (indicating an incorrect final orientation) a control systemwaits until ω₂ changes sign before firing a thruster and thereafterwaits for ω₁ to change sign, followed by a sign change for ω₂. Thesesign changes, in this order, initiates a second thruster firing in theopposite direction. The second thruster firing captures the spacecraft10 into a desired spin orientation about the major axis. The inventionsimply and efficiently, with a minimum of fuel use, permits control of afinal orientation of the stable major axis spin of a spacecraft.

According to one aspect of the invention, the method includes the stepsof detecting a spin transition and determining if the passively obtainedfinal result has the desired orientation. The desired orientationrequires no further action. However, 50% of the time the finalorientation will be incorrect, requiring that the spacecraft be respunabout the minor axis and wait for another spin transition to determineif the new final result has the desired orientation. Without control, itwill have the desired orientation 50%. of the time.

The method according to a preferred embodiment controls the subsequentspin transition to guarantee the final desired result. To accuratelycontrol the respinning and subsequent spin transition, a characteristicparameter is first decreased upon an intermediate axis spin-rate signchange. Thereafter, a sign change for ω₁, followed by a sign change forω₂, initiates an equal and opposite thruster firing which increases thecharacteristic parameter and captures the major axis spin in its desiredorientation.

The invention simply and efficiently controls spin reorientation forspinning spacecraft by complete passive control half of the time. Theother half of the time, the invention minimizes fuel usage to control afinal orientation of the spacecraft.

Referring to the remaining portions of the specification and drawingsprovides a further understanding of the nature and advantages of thepresent invention.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a graphical representation of a spacecraft with major,intermediate and minor axes X, Y and Z, respectively;

FIG. 2 is a polhode for a typical spin transition from rotation about aminor axis to rotation about a major axis;

FIG. 3A-FIG. 3F illustrate time response of spacecraft rates, angularmomentum, kinetic energy, and characteristic parameter during spintransition; specifically:

FIG. 3A is a time response of a minor axis spin rate;

FIG. 3B is a time response of an intermediate axis spin rate;

FIG. 3C is a time response of a major axis spin rate;

FIG. 3D is a time response of angular momentum;

FIG. 3E is a time response of spacecraft kinetic energy; and

FIG. 3F is a time response of the characteristic parameter;

FIG. 4 is a diagram of a polhode path when spin plurality control hasbeen implemented;

FIG. 5 is a control logic flow diagram illustrating steps for thepreferred embodiment of the present invention;

FIG. 6A-FIG. 6F are control time responses of spacecraft rates, angularmomentum, kinetic energy, and characteristic parameter during spintransition; and specifically:

FIG. 6A illustrates controlled minor axis spin rate time response;

FIG. 6B shows controlled time response for intermediate axis spin rates;

FIG. 6C illustrates major axis spin rate controlled time response;

FIG. 6D illustrates angular momentum in a controlled polarityimplementation;

FIG. 6E illustrates kinetic energy of the spacecraft time response forspin transition with control;

FIG. 6F is a controlled time response for the characteristic parameterof a spacecraft implementing spin transition control; and

FIG. 7 is a polhode path simulation for systems employing spin polaritycontrol according to a preferred embodiment of the present invention andimplementing the control logic flow of FIG. 5.

DESCRIPTION OF THE SPECIFIC EMBODIMENTS

Additional discussion of the present invention may be found in a paper"Reorientation Maneuver for Spinning Spacecraft," presented during aAAS/AIAA Astrodynamics Specialist Conference in Stowe, Vt., Aug. 7-10,1989. The paper may be obtained from the AAS Publications Office, P.O.Box 28130, San Diego, Calif. 92128, and is hereby expressly incorporatedby reference herein for all purposes. As developed in the paper, thespacecraft 10 is modelled as a rigid body with an energy sink. Anangular momentum, h, and a rotational energy, T, of the rigid body isexpressed:

    h.sup.2 =I.sub.1.sup.2 ω.sub.1.sup.2 +I.sub.2.sup.2 ω.sub.2.sup.2 +I.sub.3.sup.2 ω.sub.3.sup.2    (1)

    2T=I.sub.1 ω.sub.1.sup.2 +I.sub.2 ω.sub.2.sup.2 +I.sub.3 ω.sub.3.sup.2                                       (2)

A polhode for the rigid body traces an angular velocity vector path interms of body axis coordinates. An intersection of the momentumellipsoid (Equation 1) and the energy ellipsoid (Equation 2), identifiesthe polhode for the rigid body. Absent any energy dissipation for thespacecraft, h and T are constant, and the polhode is a closed pathcorresponding to nutational motion of the spacecraft.

For energy dissipation, T decreases and the energy ellipsoid shrinkswith time. FIG. 2 illustrates an open polhode path spiraling outwardfrom a minor axis Z, identified by its spin rate ω₃, and capturing on amajor axis X, identified by ω₁. The polhode switches from rotation aboutthe minor axis to rotation about the major axis somewhere along thespiral path. The point on which this transition occurs corresponds to acrossing of a separatrix.

An exact point on which the polhode crosses the separatrix is dependenton the initial conditions and energy dissipation characteristics of thespacecraft. Small changes in either of these parameters change the sidein which the polhode crosses the separatrix, which changes the finalspin polarity. There is a 50% chance of capturing the spin for eitherdirection of ω₁ spin. It is impossible to predict with any degree ofaccuracy the final ω₁. An example used in the following instances andfigures results from simulated initial conditions as follows:

    ______________________________________                                        Principal moment of inertia                                                                          2000    kg · m.sup.2                          about the X axis                                                              Principal moment of inertia                                                                          1500    kg · m.sup.2                          about the Y axis                                                              Principal moment of inertia                                                                          1000    kg · m.sup.2                          about the Z axis                                                              Initial Major Axis (X) Spin Rate (ω.sub.1)                                                     .1224   rad/s                                          Initial Intermediate (Y) Axis Rate (ω.sub.2)                                                   .0      rad/s                                          Initial Minor Axis (Z) Rate (ω.sub.3)                                                          2.99    rad/s                                          ______________________________________                                    

Control Logic

The control logic of the preferred embodiment guarantees desired finalspin polarity. Initially, the spacecraft 10 spins about its minor axiswith some small amount of nutation (ω₁ and/or ω₂ and ω₃ non-zero). Thespacecraft begins to transition into a flat spin, that is a spin aboutthe major axis. When the polhode crosses the separatrix, the controllogic determines the spin direction. If the spin direction for the majoraxis is correct, no action is taken. If the spin direction is incorrect,a spacecraft thruster fires to force the polhode to recross theseparatrix. Then, a short time later, an opposite thruster fires,causing the polhode to cross the separatrix again; this time the polhodeis on the desired side of the ellipsoid to provide the final desiredspin polarity.

The polhode first crosses the separatrix when ω₃ =0. One method todetect the polhode crossing the separatrix is to provide sensors whichare sensitive enough to detect ω₃ =0. Alternatively, most missions userelatively inexpensive rate gyros. Any rate gyro can be used todetermine ω₃ =0. In the preferred embodiment, existing rate gyro sensorson-board the spacecraft used for stationkeeping serve an additionalpurpose for spin polarity control. Unfortunately, the on-orbit rategyros have limited range and saturate within a limited range. Theseon-orbit rate gyros cannot accurately measure the relatively highrotational rates which occur during spin transition. However, theseon-orbit rate gyros are useful for determining a sign of the principalaxes spin rates and hence a sign change indicates when ω₃ =0. Analternate embodiment addresses use of gyros which are not preciselyaligned with the spacecraft axes. In these situations, some non-zero,but measurable rate, may indicate a separatrix crossing. The ratepassing through this measurable rate in the gyro's non-saturation regionmay indicate a separatrix crossing.

Predicting polhode crossing of the separatrix is difficult, and smallchanges in various dynamics of the system can alter final major axisspin rates. However, it is relatively easy to determine that aseparatrix crossing has occurred. FIGS. 3A through FIG. 3F illustrate atime response of spacecraft rates for spin transition as well as angularmomentum, kinetic energy, and a characteristic parameter. FIG. 3Aillustrates the time response of a minor axis spin rate. Initially, thespacecraft 10 spins about its minor axis and transitions to a spin aboutits major axis. When the minor spin rate changes sign, the polhode hascrossed the separatrix. In all cases, the polhode crosses the separatrixbefore the minor axis spin rate changes. Therefore, the minor axis ratesign change is a conservative indicator of the separatrix crossing. FIG.3A illustrates an initial minor axis spin rate, ω₃, of approximately 3rad/s which, after about 500 seconds, changes sign to indicate aseparatrix crossing. Thereafter, the minor axis spin rate willperiodically change sign, and the minor axis spin rate will decay toapproximately zero as the spacecraft transitions to a particular biasfor its major axis spin rate. FIG. 3B illustrates intermediate axis spinrate, ω₂, during spin transition. Initially, ω₂ =0 and increases to amaximum at the separatrix crossing of ω₃. Spin rate ω₂ decays to zeroafter the spin transition into the final stable major axis spin bias.Note that at the transition of the polhode crossing the separatrix, afrequency of ω₂ is lowest. Thus, the frequency of ω₂ provides analternate separatrix crossing indicator. FIG. 3C illustrates the timeresponse of the major axis spin rate (ω₁) from transition from a minoraxis spin to a stable major axis spin. Initially, the major axis spinrate periodically changes sign and its rate increases until theseparatrix crosses the polhode (≈500 seconds). After the crossing, aparticular bias of the major axis spin rate, ω₁, develops. FIG. 3Cillustrates ω₁ ≈-11/2 rad/s. As illustrated in FIG. 3D, the angularmomentum, h, remains constant during the maneuver. FIG. 3E illustratesthe kinetic energy, T, decreasing with time. FIG. 3F illustrates thechange of a characteristic parameter during spin transition.

Once the polhode has crossed the separatrix, it is possible to determinethe major axis spin rate bias. In the preferred embodiment, the sign ofthe major axis spin rate is established from a gyro measuring ω₁. If thesign of the major axis spin rate corresponds to a desired spacecraftorientation, the maneuver is complete, and transition has beensuccessfully accomplished to its desired position. If the sign is ofopposite polarity, however, the spacecraft must be reoriented.

Thruster firing readily accomplishes reorientation of the spacecraft.The thruster firing removes the major axis spin bias. Thereafter, thecontrol logic may allow another uncontrolled spin transition or controlthe subsequent spin transition. Uncontrolled spin transitions requiresubsequent checking and respins until ω₁ is correct. The preferredembodiment fires a second thruster to capture and guarantee the finalorientation of the major axis.

Spin polarity after a polhode crossing of a separatrix determineswhether thrusters are fired. If the spin polarity is correct, nothrusters are fired. If the spin polarity is incorrect, two thrusterfirings change the spin polarity and capture the polhode for a correctorientation of the major axis spin rate. The objective of the thrusterfirings is to control the polhode separatrix crossing and result in adesired direction for a major axis spin rate. Thruster firings affect a"characteristic parameter," I, that measures a distance "between thepolhode and the separatrix." The characteristic parameter, I, iswritten: ##EQU1## As an energy of the spacecraft or the spinning bodydecreases, the characteristic parameter, I, increases as shown in FIG.3F. At the separatrix crossing, I equals the principle momentum ofinertia about the intermediate axis, I₂. FIG. 3F shows that thecharacteristic parameter equals the intermediate axis inertia at theseparatrix crossing. The characteristic parameter, I, qualitativelydivides motion of the spacecraft into a regime of primarily minor axisspin (characteristic parameter is less than I₂ (the principle moment ofinertia about the intermediate axis), and a regime of primarily majoraxis spin (characteristic parameter I is greater than I₂).

An equivalent gain of a thruster firing is defined as K and is written:

    I.sup.+ =KI                                                (4)

where I⁺ is the characteristic after the firing. If I>I₂, and theobjective of the firing is to cross the separatrix, then K is chosenless than 1 such that I⁺ <I₂. For a separatrix crossing in the oppositedirection, K is chosen greater than 1.

The equivalent gain is calculated from thruster impulses, i₁, i₂, andi₃. Assuming the thruster firings are impulsive, ##EQU2## where h₁, h₂and h₃ are the components of the angular momentum prior to the firing.

For a given thruster gain value K, the timing and direction of thrusterimpulse must be determined. Since rate gyros provide only rateinformation, thrusters must be timed according to when the sign of arate changes, indicating measurement of a zero rate. Combined with threepossible impulse directions, there are nine combinations of impulsedirections and firing times. For most practical cases, an impulse aboutthe minor axis which is fired when ω₂ =0 uses the least propellant for agiven value K. The size of the impulse is calculated by substituting ω₂=0, i₁ =0, and i₂ =0 into Equation 5 and solving for i₃ : ##EQU3##

The polhode is near the separatrix when each impulse is fired; thereforesmall angle approximations may be used.

    ω.sub.2 ≈s.sub.2 ω.sub.2m tanhτ and ω.sub.3 ≈s.sub.3 ω.sub.3m sechτ                 (7)

where s₂ ω_(2m) and s₃ ω_(3m) are the signed amplitudes of the twoangular rates and τ is proportional to time. The intermediate axis spinrate is zero so tanhτ=0 and sechτ=1, resulting in ##EQU4## SubstitutingEquation 8 into Equation 6 yields ##EQU5## where ##EQU6##

FIG. 4 illustrates spin polarity control logic affecting the polhodepath. The polhode is shown folded away from the inertial ellipsoid andprojected onto a plane. The separatrix 12 resembles a figure eightwherein the angular rates are zero on vertical and horizontal lines. Thehorizontal line through the middle corresponds to ω₃ =0 and the verticallines correspond to ω₁ =0 and ω₂ =0, alternatively.

A typical polhode path is shown crossing the separatrix at 20. Thepolhode passes through ω₃ φ at 22. The sign of ω₁ determines that thespin polarity is negative, the opposite of the desired direction in thisparticular instance. At 24, when ω₂ =φ, a thruster fires to decrease I(the thruster gain K is less than 1) and the polhode goes back acrossthe separatrix at 26. The polhode then crosses ω₁ =0 at 28 and when ω₂=0 at 30, a thruster fires to increase the characteristic parameter I(the gain greater than 1) by the same amount as it was decreased in theprevious firing, thus ensuring capture on the desired side.

Determination of the value of the parameter K calculates a thrusterimpulse required to push the polhode across the separatrix.Consideration of energy dissipation rate and impulsive approximationlimits a selection of this parameter.

To ensure that the first firing forces the polhode back across theseparatrix, it must compensate for the energy loss since the polhodelast crossed the separatrix. In the worst case, the polhode crosses theseparatrix a half period from when ω₃ =φ crosses zero, so by the time ω₂=φ which initiates the thruster firing, 3/4 of a period has elapsed.

Designating Δt as the time from ω₃ =0 to ω₂ =0, the worst casecharacteristic parameter I at the first thruster firing would be##EQU7## The desired I⁺ should be large enough to ensure the separatrixis not crossed before ω₁ =0 a quarter period later, or ##EQU8##Substituting Equations 11 and 12 into Equation 4 and using Equation 3produces ##EQU9##

In order to calculate the thruster gain value K from Equation 13, energydissipation characteristics of the spacecraft at the separatrix must beknown. Characteristics can be determined experimentally or by usingtelemetry data from previous spacecraft with similar energy dissipationcharacteristics. Any uncertainty in the energy dissipation requires useof a larger impulse to ensure capture.

Each of the two thruster firings is the same in magnitude and oppositein direction. In practice, however, the second firing can be smallerthan the first firing. After the first firing, the energy dissipation ofthe spacecraft moves the polhode in the same direction as the desiredseparatrix crossing of the second firing. When the second thrusterfires, the polhode is closer to the separatrix than it was for the firstfiring, allowing use of a smaller impulse.

Due to the limited torque capability of the thrusters, the actualfirings are not impulsive. This results in a loss of efficiency,preventing achievement of the desired I⁺. Thruster firings initiatedupon sign change of ω₂ require completion of the firing before ω₃changes sign. Otherwise, the firing will not produce the desired effect.If the required firing is too large for a given thruster configuration,the reduction of the initial spin rate contracts the thruster firingtime proportionally (See Equation 9).

FIG. 5 is a flow diagram for the control logic used in a spin transitioncontrol according to the preferred embodiment of the present invention.Initially, a control system monitors ω₃ from a gyro. An ω₃ sign change,causes measurement of the sign of ω₁. If ω₁ has the desired sign, thespin transition was successful. If the ω₁ is of opposite sign, however,the controller waits for a change in sign of ω₂ and fires a firstthruster which reduces the characteristic parameter I according toEquation 9. The control system then waits for a subsequent zero crossingof ω₁ followed by a sign change of ω₂ to initiate a torque (secondthruster firing) about the minor axis to guarantee capture.

FIG. 6 illustrates a controlled time response of spacecraft spin rates,angular momentum, energy and characteristics parameter during controlledspin transition. Specifically, FIG. 6A illustrates the time response ofa minor axis spin rate. FIG. 6B illustrates an intermediate axis spinrate time response, FIG. 6C illustrates a major axis spin rate timeresponse showing a major axis spin rate resulting in a bias differentfrom that of the illustration in FIG. 2C. FIG. 2D illustrates theangular momentum of the spacecraft time response. FIG. 6E illustratestime response of the kinetic energy of the system showing, at spintransition, the thruster firing momentarily increasing the kineticenergy. FIG. 6F illustrates the change in the characteristic parametertime response with the control showing a first decrease and thenincrease in the characteristic parameter. The decrease of thecharacteristic parameter takes the parameter below the intermediate axisinertia value and then the subsequent firing returns the characteristicparameter above the intermediate axis momentum inertia.

FIG. 7 is an illustration of a polhode path simulation for systemsemploying spin polarity control according to the preferred embodiment ofthe present invention and implementing the control logic flow of FIG. 5.The polhode path of FIG. 7 illustrates control spin transition for thesame initial conditions of mass properties as the system illustrated inFIG. 2. The control system of FIG. 5 ensures a positive final spin ratefor the major axis (ω₁ >0). The polhode first crosses the separatrix at40. When ω₃ =0 (at 42), ω₁ <0. When ω₂ crosses zero (at step 44), athruster firing causes the polhode to recross the separatrix at 46.Next, ω₁ crosses zero at 48, signaling successful completion of theseparatrix crossing. At 50, ω₂ crosses zero, and a second firingincreases the characteristic parameter I, and the polhode captures onthe desired side. The time response curves of FIG. 6A through 6F andFIG. 7 shows that the ω₁ response initially captures on the negativeside and then is pushed by thruster firing to the positive side. Theangular momentum and kinetic energy change each time the thruster fires,with the parameter I decreasing and then increasing.

A further level of sophistication is possible with the presentinvention. Typically, a spin transition maneuver is one of the firstmaneuvers conducted. It is also likely that some of the thrusters willbe unused before controlling spin transitions. It is possible that theremay be some thruster failure, complete or partial, which will notproperly orient the spacecraft. Thus, spacecraft 10 desirably includesautonomous operation of the control logic and spin transition mechanism.Spin transition after launch vehicle separation is the first time thatmost of the gyros, thrusters, on-board processor, etc., are used andthere usually is no ground telemetry or command during this maneuver.

The dashed polhode path in FIG. 4, illustrating steps 28' and 30',describe an alternate path followed if the first thruster firing fails.The alternate path ensures autonomous operation. If the first thrusterfiring fails, ω₃ crosses zero 28' before ω₁. Upon ω₃ crossing before ω₁the control system may switch autonomously to a backup string ofthrusters and fire a larger impulse at 30'.

The dotted line in FIG. 5 shows the autonomous thruster failuredetection logic. After the first firing, the controller monitors both ω₁and ω₃. If ω₁ crosses first, then the path follows the regular logic. Ifω₃ crosses first, then the thrusters are reconfigured and a largerimpulse is fired. The dotted path illustrated in FIG. 5 after the secondfiring ensures proper operation upon failure of the second thruster. Inpractice, limiting the number of paths through the flow diagramprecludes the possibility of limit cycles.

The spin transition maneuver, when augmented with two thruster firingsbased on gyro measurements, provides the predetermined final spinpolarity for a major axis spin that is stable for an energy dissipativesystem. The control logic implementing the flow diagram of FIG. 5 usesrate sign changes to determine separatrix crossings and timings forthruster firings. The control logic sizes each thruster firing basedupon estimates of the energy dissipation in the spacecraft. Limitationin the torque capability of a particular thruster configuration mayconstrain the maximum controllable initial spin rate.

In conclusion, the present invention simply and efficiently provides amethod to reorient a spinning spacecraft during a spin transition. Fueluse is minimized without requiring extra sensing equipment. The above isa complete description of the preferred embodiments of the invention. Itis possible to use various alternatives, modifications, and equivalentsin the practice of the present invention, some of which have beendescribed herein. For example, other manners of directly sensing aseparatrix crossing may trigger thruster firings. As discussed, thecontrol logic may allow a single thruster firing to decrease thecharacteristic parameter and subsequently permit an uncontrolled spintransition back to a major axis spin bias. Each uncontrolled spintransition has a 50% chance of properly orienting itself without activecontrol. Two thruster firings can guarantee capture in a desiredconfiguration for a major axis bias orientation. However, the abovedescription of the preferred embodiments does not limit the scope of theinvention. The appended claims define this scope.

What is claimed is:
 1. A method of effecting spin transitioning of anobject having a minor axis, an intermediate axis, and a major axis froma spin about the minor axis to a particular orientation of spin aboutthe major axis, comprising the steps of:a) detecting transition of thespin of the object to a spin bias about the major axis; b) determiningthat said major axis spin bias is not a desired spin bias; c) applying acontrol impulse to said object to remove said spin bias if said spinbias is not said desired spin bias; and d) thereafter repeating steps a)through c) until said object has said desired major axis spin bias.
 2. Amethod of effecting spin transitioning of an object, having a minoraxis, an intermediate axis, and a major axis, from a predominate minoraxis spin to a particular major axis spin orientation, comprising thesteps of:a) detecting a transition of spin of the object from thepredominate minor axis spin to a major axis spin bias; b) determiningthat said major axis spin bias is not the particular major axis spinorientation; c) applying a first control impulse to said object toremove said major axis spin bias if said major axis spin bias is notsaid particular major axis spin orientation; and d) applying a secondcontrol impulse to said object to provide said object with saidparticular major axis spin orientation.
 3. A method of effecting spintransitioning of an object, having a minor axis, an intermediate axisand a major axis with a spin rate measuring device for each of the spinaxes of the object, and a characteristic parameter, from a predominateminor axis spin to a particular orientation of a major axis spin,comprising the steps of:detecting a first minor axis spin rate signchange for the minor axis spin, and thereafter testing a sign of a majoraxis spin rate to determine that the object does not have the particularmajor axis spin orientation; and if said major axis spin rate sign doesnot indicate the object has the particular major axis spin orientation,then thereafter:applying a first control impulse to decrease acharacteristic parameter by a particular amount when an intermediateaxis spin rate changes sign; and applying a second control impulse toincrease said characteristic parameter by about said particular amountfollowing an intermediate axis spin rate sign change sign after a minoraxis spin rate sign change.
 4. A method of effecting spin transitioningof an object having a minor axis, an intermediate axis, and a major froma spin about the minor axis to a particular orientation of spin aboutthe major axis, comprising the steps of:a) detecting a spin bias aboutthe major axis after a spin transition of the object; b) determiningthat said major axis spin bias is not a desired spin bias; c) removingsaid major axis spin bias if said major axis spin bias is not saiddesired spin bias; and d) thereafter repeating steps a) through c) untilsaid object has said desired major axis spin bias.
 5. The method ofclaim 4 wherein said removing step further comprises the step of:firinga first thruster to decrease a characteristic parameter of the object bya first particular amount.
 6. A method for effecting a desired spintransition, comprising the steps of:providing a spinning objectcharacterized by a minor axis, an intermediate axis, and a major axis,said object having a predominate minor axis spin; establishing a firstseparatrix crossing for a polhode associated with said spinning object,said polhode identified by an intersection of a momentum ellipsoid andan energy ellipsoid for said spinning object; thereafter determiningthat said spinning object does not have a desired major axis spin bias;and thereafter if said major axis spin bias does not have said desiredmajor axis spin bias:decreasing a characteristic parameter of saidspinning object to produce a second separatrix crossing; and repeatingsaid establishing, determining and decreasing steps until said spinningobject has said desired major axis spin bias.
 7. A method for effectinga desired spin transition, comprising the steps of:providing a spinningobject characterized by a minor axis, an intermediate axis, and a majoraxis, said object having a predominate minor axis spin; establishing afirst separatrix crossing for a polhode associated with said spinningobject, said polhode identified by an intersection of a momentumellipsoid and an energy ellipsoid for said spinning object; thereafterdetermining that said spinning object does not have a desired major axisspin bias; and thereafter if said major axis spin bias does not havesaid desired major axis spin bias:decreasing a characteristic parameterof said spinning object to produce a second separatrix crossing; andthereafter increasing said characteristic parameter of said spinningobject to produce a third separatrix crossing which provides saidspinning object with said desired major axis spin bias.
 8. The method ofclaim 7 wherein said establishing an determining steps each comprise thestep of:monitoring a gyroscope rate output for an indication of a ratesign change.
 9. The method of claim 7 wherein said establishing anddetermining steps each comprise the step of:monitoring a gyroscope rateoutput for an indication of a rate passing through a predetermined valuewithin a non-saturation range of said gyroscope.
 10. The method of claim7 wherein said decreasing and increasing steps each comprise the stepof:firing a thruster to effect rotation about a prespecified axis. 11.The method of claim 7 wherein said establishing step comprisesmonitoring a minor axis spin rate to detect a prespecified change insaid minor axis spin rate.
 12. The method of claim 7 wherein saiddetermining step comprises monitoring a major axis spin rate to detect aprespecified bias for said major axis spin rate.
 13. A method foreffecting a desired spin transition, comprising the steps of:providing aspinning object characterized by a minor axis, an intermediate axis, anda major axis, said object having a predominate minor axis spin;establishing a first separatrix crossing for a polhode associated withsaid spinning object, said polhode identified by an intersection of amomentum ellipsoid and an energy ellipsoid for said spinning object;thereafter determining that said spinning object does not have a desiredmajor axis spin bias; and thereafterinitiating a decrease in acharacteristic parameter of said spinning object to produce a secondseparatrix crossing; and thereafter initiating an increase in saidcharacteristic parameter of said spinning object to produce a thirdseparatrix crossing which provides said spinning object with saiddesired major axis spin bias.
 14. The method of claim 13 wherein saidcharacteristic parameter decrease initiating step is responsive to apredetermined rate change of a spin rate of said intermediate axis. 15.The method of claim 13 wherein said characteristic parameter increaseinitiating step is responsive to a predetermined rate change of a spinrate of said intermediate axis after a predetermined rate change of aspin rate of said major axis.
 16. The method of claim 13 furthercomprising the steps of:detecting a failure of said characteristicparameter decrease initiating step to produce a second separatrixcrossing; and reinitiating a decrease in said characteristic parameterto produce said second separatrix crossing within a predeterminedinterval of time if said failure is detected.
 17. The method of claim 13further comprising the steps of:detecting a failure of saidcharacteristic parameter increase initiating step to produce a thirdseparatrix crossing; and reinitiating an increase in said characteristicparameter to produce said third separatrix crossing within apredetermined interval of time if said failure is detected.
 18. Themethod of claim 13 further comprising the steps of:detecting a firstfailure of said characteristic parameter decrease initiating step toproduce a second separatrix crossing; reinitiating a decrease in saidcharacteristic parameter to produce said second separatrix crossingwithin a predetermined interval of time if said first failure isdetected; detecting a second failure of said characteristic parameterincrease initiating step to produce a third separatrix crossing; andreinitiating an increase in said characteristic parameter to producesaid third separatrix crossing within a predetermined interval of timeif said second failure is detected.
 19. A method of effecting spintransitioning of an object having a minor axis, an intermediate axis,and a major axis from a spin about the minor axis to a particularorientation of spin about the major axis, comprising the steps of:a)monitoring, without exerting active major spin axis orientation control,said object for a transition of the spin of the object to a spin biasabout the major axis; and thereafter b) determining that said major axisspin bias does not have a desired spin bias; c) applying a first controlimpulse to said object to remove said spin bias only if said spin biasis not said desired spin bias; and thereafter d) applying a secondcontrol impulse to said object to orient said major spin axis bias equalto said desired spin bias.